1. Field of the Invention
The invention relates to a closed loop control system, and more particularly to the loop bandwidth of a closed loop control system.
2. Description of the Related Art
Automatic Frequency Control (AFC) is a common mechanism used in wireless communication systems. AFC eliminates the frequency offset error between a transmitter side and a receiver side, which mainly results from component mismatchimg and inaccuracy, different operating environments, or the Doppler channel effect. The frequency offset error is undesirable in the receiver system, because a small frequency offset error may cause severe system performance degradation.
There are two main considerations to the performance of an AFC mechanism. One is the convergence speed, which is how fast the frequency offset error can be reduced by AFC mechanism to an acceptable level. The other is the residual frequency offset amount after AFC has acquired most of the frequency of the transmitter side, wherein the residual frequency offset amount is the minimized level of the frequency offset error and represents the stability of the output signal of the closed loop control system. Both considerations are important in AFC design. There is, however, a tradeoff between the convergence speed and the output signal stability in ordinary AFC mechanisms. The higher the convergence speed, the lower the output signal stability. The reasons for this are provided in the following.
FIG. 1 is a closed loop control system 100, which is generally used to implement an AFC mechanism. The closed loop control system 100 includes a compensator 102, an error detector 104, a loop filter 106, and a delay module 108. The input signal of the closed loop control system is first processed with a reference target signal (not shown in the FIG. 1) by the error detector 104 to generate an error signal. In an ordinary closed loop control system 100, the reference target signal may be the feedback signal from the feedback loop or the output signal of the closed loop control system 100, and the error signal may be the difference between the input signal and the reference target signal. Thus, the error signal reflects the convergence status of the output signal of the closed loop control system 100.
The error signal is then delivered to a loop filter 106, which filters the error signal in the feedback loop to generate a feedback signal. The delay module 108 then delays the feedback signal to mimic a practical closed loop with fixed loop latency. The compensator 102 then compensates the input signal of the closed loop control system 100 with the feedback signal to generate the output signal of the closed loop control system 100. The closed loop control system 100 can be a phase locked loop (PLL) or a frequency locked loop (FLL).
FIG. 2 and FIG. 3 respectively show a phase locked loop system 200 and a frequency locked loop system 300. The input signal of the PLL system 200 is a phase signal θi, and the output signal of the PLL system 200 is a phase signal θo. The phase detector 204 detects the phase error, and the loop filter 206 generates a feedback signal Δθ with the phase error. The voltage controlled oscillator 202 then compensates the input signal θi with the delayed feedback signal Δθ to generate the output signal θo. Accordingly, The input signal of the FLL system 300 is a frequency signal fi, and the output signal of the FLL system 300 is a frequency signal fo. The frequency discriminator 304 detects the frequency error, and the loop filter 306 generates a feedback signal Δf with the frequency error. The voltage controlled oscillator 302 then compensates the input signal fi with the delayed feedback signal Δf to generate the output signal fo.
A main characteristic of the loop filter 106 is its loop bandwidth, which represents the filtered amount of the input signal to form the feedback signal. When the loop bandwidth is larger, the filtered range of the feedback signal is larger. Thus, when the output signal is compensated with the feedback signal, the output signal rapidly reaches steady state. In other words, the convergence speed of the closed loop control system is faster. Because the loop bandwidth is fixed, however, the feedback signal cannot be precisely adjusted when the output signal is steady, and the output signal is less stable. On the contrary, when the loop bandwidth is smaller, the filtered range of the feedback signal is smaller. When the output signal is steady, the stability of the output signal is higher, but the output signal more slowly reaches steady state. In other words, the convergence speed of the closed loop control system is lower. Thus, there is a tradeoff between the convergence speed and the output signal stability in ordinary closed loop control systems.
To solve this problem, the invention provides a method for dynamically changing the loop bandwidth of a closed loop control system. The signal convergence process of a closed loop control system can be classified into two phases. When the compensating process first begins, the output signal is not yet fully compensated, and the error signal is quite large. This phase is called “acquisition state”. In this phase, the loop bandwidth should be large enough to reduce the error signal to a tolerable level as rapidly as possible. Thus, the system waiting time can be minimized, and the convergence speed is more important than the output signal stability in this phase. When the loop is almost converged, the output signal reaches the steady state and can be further processed. This phase is called “tracking state”. In this phase, the loop bandwidth should be small enough to finely adjust the feedback signal, and a more stable output signal is generated. Thus, the error signal can be minimized, and the output signal stability is more important than the convergence speed in this phase. Thus, the invention combines both the advantages of fast convergence speed and high output signal stability.